The entity we need first, is a move_rope. This will be the upper end of the rope.
Name it rope1 (or similar) and set
Next KeyFrame to rope2. Choose Subdivision values as you like, you might leave them at the default.

The next entity is the keyframe_rope, the ending point of the rope.
It is called rope2, so that it completes the rope that started with the move_rope. Don't forget to set
Parent: box

Next, make a little brush, about 16x16x16 and center it onto the keyframe_rope. Texture it with the nodraw texture, and click ctrl + t to make it a func_physbox, adjusting these values: